A new general expression for 2-channel FIR paraunitary filterbanks

This paper provides a new explicit expression for all real FIR paraunitary filters. From this we derive a new procedure for the design of the L components of any 2-channel FIR orthogonal L-tap filter. The input of this algorithm is any set of L/2 free parameters. Moreover, our procedure provides a parameterization of all orthogonal filters directly, with no need for iterations. For the special case of low-pass paraunitary filters, we obtain a fast new design algorithm. Simplified expressions for the frequency response of paraunitary filters are also provided. In addition to these improvements, our results also yield exact solutions of a particular set of Bezout polynomial equations.